Question: If $x \star y = 3x-6y$ and $x \barwedge y = x+3y$, find $(-4 \star -6) \barwedge 2$.
Answer: First, find $-4 \star -6$ $ -4 \star -6 = (3)(-4)-(6)(-6)$ $ \hphantom{-4 \star -6} = 24$ Now, find $24 \barwedge 2$ $ 24 \barwedge 2 = 24+(3)(2)$ $ \hphantom{24 \barwedge 2} = 30$.